Mathematics
Arithmetic performance depends on the neural processing across distinct brain regions. This study investigates whether clustering coefficients (CCs), a graph theory metric for centrality, re…
Mathematics
Two - qubit gates drive the power of quantum circuits, but finding new universal gates remains challenging. In this study, we developed an evolutionary computational framework to systematica…
Mathematics
This project investigated a cryptographic framework for cybersecurity utilizing a pair of a field-defining monic irreducible polynomial f(x) and an associated multiplier polynomial k(x) as a…
Mathematical Sciences (Junior Division)
We use AI in daily life, sometimes involuntarily (such as Google Search Overview). However, some AI models might be more reliable or structured than others. In this project, we tested six di…
Mathematics
This project investigates how player market value in professional soccer is shaped by long-term ability and short-term seasonal performance. Transfer markets often show inconsistencies betwe…
Mathematical Sciences (Senior Division)
Alzheimer’s disease (AD) affects 55 million people worldwide and is a major contributor to the global burden on healthcare systems, families, and caregivers. It has been found that detectabl…
Mathematics
Traffic congestion is one of the most persistent urban challenges in the United States, costing Atlanta-area commuters over 65 hours and approximately $1,164 per driver in 2024. Traffic cong…
Mathematical Sciences (Junior Division)
Fourth Award
Humans inherently communicate through body movement. Therefore bodily expressions serve as a powerful but often subconscious channel for emotion and social signaling. Despite progress in vis…
Mathematics
Purpose: A set of two new operators contribute to the development of a new theorem on jumpability that, together with a six-fold characterization of dimensional-expansions, are used to estab…
Mathematics
One of the central open problems in operator theory and PT-symmetric quantum mechanics is how to construct metric operators explicitly for non-Hermitian operators acting in spaces with an in…
Mathematics
Urban accessibility optimization is a pressing challenge for sustainable urban development. Classical graph-theoretical methods, such as the Steiner tree problem, provide a framework for con…
Mathematics
Fourth Award
The theory of isogonal cubics is a powerful tool in proving the relations of angles. A part of the theory is deduced from Newton's theorems on conics. It is known that Newton's theorems can…
Mathematical Sciences (Junior Division)
Artificial intelligence (AI) has become quite common and can be found doing many different things. Around 73% of Americans show a willingness to incorporate AI into their daily lives (Pew Re…
Mathematical Sciences (Junior Division)
First Award
Purpose: The knowledge of the relationship between an integer n and its divisors aids number-theoretic research in integer partitions, prime number search, and subset sum problems. Prior wor…
Mathematics
Modern financial markets are complex, interconnected systems where localized stress can amplify into system-wide instability. Traditional risk measures, such as volatility indices, quantify…
Mathematical Sciences (Junior Division)
This project explores the simplified question: “How can we use computer model variables to predict the effectiveness of social distancing compliance using autonomous dotted agents to simulat…
Mathematics
First Award
An equation f(x)=a, where f is a complex meromorphic function and a is a parameter, is solvable in elementary functions if the inverse map x=f^{-1}(a) can be expressed as a finite compositio…
Mathematical Sciences (Senior Division)
Fourth Award
The research goal is to develop an original method to fill some long-term existing gaps in statistical inferences on the self-similar stochastic processes. Self-similar processes are stochas…
Mathematical Sciences (Senior Division)
The spin representation is a mathematical object parametrizing the spin states of multiple-electron systems, introduced by Cartan in 1913 and applied to physics by Dirac in 1928. It has a du…
Mathematics
Third Award
This project focuses on the Repelling Propellers Problem, an unsolved problem proposed by Professor James Propp. The question investigates how same-sign, equally charged/spaced points behave…
Mathematical Sciences (Senior Division)
First Award
This project focuses on the Repelling Propellers Problem, an unsolved problem proposed by Professor James Propp. The question investigates how same-sign, equally charged/spaced points behave…
Mathematics
Fourth Award
This paper investigates invariants for distinguishing virtual knots. The existing H_MJ polynomial suffers from a structural weakness: when its base polynomial evaluates to zero, essential cr…
Mathematics
Second Award
Cryptographic systems securing global communications depend on computationally hard mathematical problems. Yet, the divisibility structure of combinatorial objects like Pascal’s Triangle rem…
Mathematics
Airlines have increasingly adopted flexible refund policies that allow passengers to cancel tickets in exchange for time-limited travel credits. While these policies reduce customer risk, th…
Mathematical Sciences (Senior Division)
Honorable_mention Award
Airlines have increasingly introduced flexible refund policies that allow passengers to cancel tickets and receive time-limited travel credits. These policies introduce additional uncertaint…
Mathematical Sciences (Junior Division)
Second Award
VisionSpeak: A Wearable Edge-AI System That Describes the World Through Synthesized Speech for the Visually Impaired Shreyan Biswas Our project aims to enhance independent mobility and safet…
Mathematical Sciences (Junior Division)
The objective of this experiment was to investigate how common materials, specifically, metal, wood, and cardboard, affect the strength and speed of Wifi. As wireless technology becomes more…
Mathematics
Understanding interactions between the spread of multiple pathogens during an epidemic is crucial to assessing the severity of infections in living communities. I created two novel Multiplex…
Mathematics
Fourth Award
High-dimensional data is often difficult to analyze because of the exponential growth of the size of the space in which the data lives as the dimension increases. One example of high-dimensi…
Mathematics
Third Award
In this study, I present a novel approach for model compression to reduce the size of neural network models. In recent years, with the rise of LLMs such as ChatGPT, deep learning models have…